The propagation of cylindrical shock wave in rotational axisymmetric perfect gas under isothermal flow condition with azimuthal magnetic field is investigated. Distributions of gas dynamical quantities are discussed. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to power law with distance from the axis of symmetry in the undisturbed medium. Approximate analytical solutions are obtained by expanding flow variables in power series. Zeroth-order and first-order approximations are discussed with the aid of power series method. Solutions for zeroth-order approximation are constructed in approximate analytical form. The effect of flow parameters namely: shock Cowling number $$C_{0}$$, ambient density variation index q and adiabatic exponent $$\gamma $$ are studied on the flow variables. Consideration of magnetic pressure increases the total energy of disturbance of zeroth order while with increase in ambient density variation index or adiabatic exponent, the total energy of disturbance decreases.

中文翻译：

---

具有方位磁场的旋转轴对称完美气体中激波的近似解析解：等温流

研究了圆柱激波在具有方位磁场的等温流动条件下在旋转轴对称完美气体中的传播。讨论了气体动力学量的分布。假设密度、磁压、方位角流体速度和轴向流体速度根据幂律随与未受干扰介质中的对称轴的距离而变化。通过在幂级数中展开流动变量来获得近似解析解。借助幂级数方法讨论了零阶和一阶近似。零阶近似的解以近似解析形式构建。流动参数的影响即：冲击整流罩数$$C_{0}$$，对流动变量研究了环境密度变化指数q和绝热指数$$\gamma $$。考虑磁压增加了零级扰动的总能量，而随着环境密度变化指数或绝热指数的增加，扰动的总能量减小。